AI 中文总结
研究广义泊松西格玛模型这一全纯拓扑场论，探讨其与全纯拓扑因式分解代数变形量子化的关系，用 Koszul 对偶方法研究边界代数得量子群，通过多种例子阐释一般框架。
AI 中文摘要
在这项工作中，我们引入并研究了一族全纯拓扑场论，即广义泊松西格玛模型。这些理论是二维泊松西格玛模型的高维类似物，其目标数据由平移手征泊松结构编码。我们研究它们与全纯拓扑因式分解代数的变形量子化的关系。在此过程中，基于导出代数几何中的相关概念，系统地构建了扩展对象，包括界面、丰富边界和缺陷。我们采用 Koszul 对偶方法研究边界代数，得到各种版本的量子群。通过一系列例子说明了一般框架，包括超对称规范理论的扭量以及超对称起源之外的例子。
英文摘要
In this work we introduce and study a family of holomorphic--topological field theories, which we call generalized Poisson sigma models. These theories are higher-dimensional analogues of the two-dimensional Poisson sigma model, with target data encoded by shifted chiral Poisson structures. We investigate their relationship with deformation quantizations of holomorphic--topological factorization algebras. Along the way, we give a systematic construction of extended objects, including interfaces, enriched boundaries and defects based on relevant notions in derived algebraic geometry. We employ Koszul-duality methods to study boundary algebras, yielding various versions of quantum groups. We illustrate the general framework through a range of examples, including twists of supersymmetric gauge theories as well as examples beyond the supersymmetric origin.
Comments132 pages, 28 figures
